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Volumn 199, Issue 1, 2011, Pages 291-328

Optimal Time Decay of the Vlasov-Poisson-Boltzmann System in ℝ3

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EID: 78650993289     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-010-0318-6     Document Type: Article
Times cited : (110)

References (33)
  • 2
    • 12844275468 scopus 로고    scopus 로고
    • On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation
    • Desvillettes L., Villani C.: On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation. Invent. Math. 159(2), 245-316 (2005).
    • (2005) Invent. Math. , vol.159 , Issue.2 , pp. 245-316
    • Desvillettes, L.1    Villani, C.2
  • 3
    • 84990553444 scopus 로고
    • Global weak solution of Vlasov-Maxwell systems
    • DiPerna R. J., Lions P.-L.: Global weak solution of Vlasov-Maxwell systems. Commun. Pure Appl. Math. 42, 729-757 (1989).
    • (1989) Commun. Pure Appl. Math. , vol.42 , pp. 729-757
    • Diperna, R.J.1    Lions, P.-L.2
  • 4
    • 0001089576 scopus 로고
    • On the Cauchy problem for Boltzmann equation: global existence and weak stability
    • DiPerna R. J., Lions P.-L.: On the Cauchy problem for Boltzmann equation: global existence and weak stability. Ann. Math. 130, 321-366 (1989).
    • (1989) Ann. Math. , vol.130 , pp. 321-366
    • Diperna, R.J.1    Lions, P.-L.2
  • 5
    • 64749085031 scopus 로고    scopus 로고
    • Hypocoercivity for kinetic equations with linear relaxation terms
    • Dolbeault J., Mouhot C., Schmeiser C.: Hypocoercivity for kinetic equations with linear relaxation terms. C. R. Acad. Sci. Paris 347, 511-516 (2009).
    • (2009) C.R. Acad. Sci. Paris , vol.347 , pp. 511-516
    • Dolbeault, J.1    Mouhot, C.2    Schmeiser, C.3
  • 7
    • 67651232554 scopus 로고    scopus 로고
    • Stability of the Boltzmann equation with potential forces on torus
    • Duan R.-J.: Stability of the Boltzmann equation with potential forces on torus. Phys. D Nonlinear Phenom. 238, 1808-1820 (2009).
    • (2009) Phys. D Nonlinear Phenom. , vol.238 , pp. 1808-1820
    • Duan, R.-J.1
  • 8
    • 77950787117 scopus 로고    scopus 로고
    • Stability of the one-species Vlasov-Poisson-Boltzmann system
    • Duan R.-J., Yang T.: Stability of the one-species Vlasov-Poisson-Boltzmann system. SIAM J. Math. Anal. 41(6), 2353-2387 (2010).
    • (2010) SIAM J. Math. Anal. , vol.41 , Issue.6 , pp. 2353-2387
    • Duan, R.-J.1    Yang, T.2
  • 9
    • 33747711299 scopus 로고    scopus 로고
    • Boltzmann equation with external force and Vlasov-Poisson-Boltzmann system in infinite vacuum
    • Duan R.-J., Yang T., Zhu C.-J.: Boltzmann equation with external force and Vlasov-Poisson-Boltzmann system in infinite vacuum. Discrete Contin. Dyn. Syst. 16, 253-277 (2006).
    • (2006) Discrete Contin. Dyn. Syst. , vol.16 , pp. 253-277
    • Duan, R.-J.1    Yang, T.2    Zhu, C.-J.3
  • 10
    • 36448982541 scopus 로고    scopus 로고
    • Optimal decay estimates on the linearized Boltzmann equation with time-dependent forces and their applications
    • Duan R.-J., Ukai S., Yang T., Zhao H.-J.: Optimal decay estimates on the linearized Boltzmann equation with time-dependent forces and their applications. Commun. Math. Phys. 277(1), 189-236 (2008).
    • (2008) Commun. Math. Phys. , vol.277 , Issue.1 , pp. 189-236
    • Duan, R.-J.1    Ukai, S.2    Yang, T.3    Zhao, H.-J.4
  • 11
    • 0033244167 scopus 로고    scopus 로고
    • Decay of the linearized Boltzmann-Vlasov system
    • Glassey R., Strauss W.: Decay of the linearized Boltzmann-Vlasov system. Transp. Theory Statist. Phys. 28, 135-156 (1999).
    • (1999) Transp. Theory Statist. Phys. , vol.28 , pp. 135-156
    • Glassey, R.1    Strauss, W.2
  • 12
    • 0033460696 scopus 로고    scopus 로고
    • Perturbation of essential spectra of evolution operators and the Vlasov-Poisson-Boltzmann system
    • Glassey R., Strauss W.: Perturbation of essential spectra of evolution operators and the Vlasov-Poisson-Boltzmann system. Discrete Contin. Dyn. Syst. 5, 457-472 (1999).
    • (1999) Discrete Contin. Dyn. Syst. , vol.5 , pp. 457-472
    • Glassey, R.1    Strauss, W.2
  • 13
    • 8844227476 scopus 로고    scopus 로고
    • The Boltzmann equation in the whole space
    • Guo Y.: The Boltzmann equation in the whole space. Indiana Univ. Math. J. 53, 1081-1094 (2004).
    • (2004) Indiana Univ. Math. J. , vol.53 , pp. 1081-1094
    • Guo, Y.1
  • 14
    • 0036328887 scopus 로고    scopus 로고
    • The Vlasov-Poisson-Boltzmann system near Maxwellians
    • Guo Y.: The Vlasov-Poisson-Boltzmann system near Maxwellians. Commun. Pure Appl. Math. 55(9), 1104-1135 (2002).
    • (2002) Commun. Pure Appl. Math. , vol.55 , Issue.9 , pp. 1104-1135
    • Guo, Y.1
  • 15
    • 0035531905 scopus 로고    scopus 로고
    • The Vlasov-Poisson-Boltzmann system near vacuum
    • Guo Y.: The Vlasov-Poisson-Boltzmann system near vacuum. Commun. Math. Phys. 218(2), 293-313 (2001).
    • (2001) Commun. Math. Phys. , vol.218 , Issue.2 , pp. 293-313
    • Guo, Y.1
  • 17
    • 0009326251 scopus 로고
    • The Boltzmann equation and thirteen moments
    • Kawashima S.: The Boltzmann equation and thirteen moments. Japan J. Appl. Math. 7, 301-320 (1990).
    • (1990) Japan J. Appl. Math. , vol.7 , pp. 301-320
    • Kawashima, S.1
  • 19
    • 0346498040 scopus 로고    scopus 로고
    • Energy method for the Boltzmann equation
    • Liu T.-P., Yang T., Yu S.-H.: Energy method for the Boltzmann equation. Phys. D 188(3-4), 178-192 (2004).
    • (2004) Phys. D , vol.188 , Issue.3-4 , pp. 178-192
    • Liu, T.-P.1    Yang, T.2    Yu, S.-H.3
  • 20
    • 1842591085 scopus 로고    scopus 로고
    • Boltzmann equation: micro-macro decompositions and positivity of shock profiles
    • Liu T.-P., Yu S.-H.: Boltzmann equation: micro-macro decompositions and positivity of shock profiles. Commun. Math. Phys. 246(1), 133-179 (2004).
    • (2004) Commun. Math. Phys. , vol.246 , Issue.1 , pp. 133-179
    • Liu, T.-P.1    Yu, S.-H.2
  • 21
    • 8744245272 scopus 로고    scopus 로고
    • The Green's function and large-time behavior of solutions for the one-dimensional Boltzmann equation
    • Liu T.-P., Yu S.-H.: The Green's function and large-time behavior of solutions for the one-dimensional Boltzmann equation. Commun. Pure Appl. Math. 57, 1543-1608 (2004).
    • (2004) Commun. Pure Appl. Math. , vol.57 , pp. 1543-1608
    • Liu, T.-P.1    Yu, S.-H.2
  • 23
    • 0034348887 scopus 로고    scopus 로고
    • On the initial boundary value problem for the Vlasov-Poisson-Boltzmann system
    • Mischler S.: On the initial boundary value problem for the Vlasov-Poisson-Boltzmann system. Commun. Math. Phys. 210, 447-466 (2000).
    • (2000) Commun. Math. Phys. , vol.210 , pp. 447-466
    • Mischler, S.1
  • 24
    • 33645088687 scopus 로고    scopus 로고
    • Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus
    • Mouhot C., Neumann L.: Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus. Nonlinearity 19(4), 969-998 (2006).
    • (2006) Nonlinearity , vol.19 , Issue.4 , pp. 969-998
    • Mouhot, C.1    Neumann, L.2
  • 26
    • 33749987309 scopus 로고    scopus 로고
    • The Vlasov-Maxwell-Boltzmann system in the whole space
    • Strain R. M.: The Vlasov-Maxwell-Boltzmann system in the whole space. Commun. Math. Phys. 268(2), 543-567 (2006).
    • (2006) Commun. Math. Phys. , vol.268 , Issue.2 , pp. 543-567
    • Strain, R.M.1
  • 27
    • 33644808362 scopus 로고    scopus 로고
    • Almost exponential decay near Maxwellian, Comm
    • Strain R. M., Guo Y.: Almost exponential decay near Maxwellian, Comm. P. D. E. 31(3), 417-429 (2006).
    • (2006) P.D.E. , vol.31 , Issue.3 , pp. 417-429
    • Strain, R.M.1    Guo, Y.2
  • 28
    • 37449012365 scopus 로고    scopus 로고
    • Exponential decay for soft potentials near Maxwellian
    • Strain R. M., Guo Y.: Exponential decay for soft potentials near Maxwellian. Arch. Ration. Mech. Anal. 187, 287-339 (2008).
    • (2008) Arch. Ration. Mech. Anal. , vol.187 , pp. 287-339
    • Strain, R.M.1    Guo, Y.2
  • 29
    • 0000824099 scopus 로고
    • On the existence of global solutions of mixed problem for non-linear Boltzmann equation
    • Ukai S.: On the existence of global solutions of mixed problem for non-linear Boltzmann equation. Proc. Japan Acad. 50, 179-184 (1974).
    • (1974) Proc. Japan Acad. , vol.50 , pp. 179-184
    • Ukai, S.1
  • 30
    • 36448945743 scopus 로고    scopus 로고
    • 3: global and time-periodic solutions
    • 3: global and time-periodic solutions. Anal. Appl. 4, 263-310 (2006).
    • (2006) Anal. Appl. , vol.4 , pp. 263-310
    • Ukai, S.1    Yang, T.2
  • 31
    • 75249084216 scopus 로고    scopus 로고
    • Hypocoercivity
    • Villani C.: Hypocoercivity. Mem. Am. Math. Soc. 202(950), iv+141 (2009).
    • (2009) Mem. Am. Math. Soc. , vol.202 , Issue.950
    • Villani, C.1
  • 32
    • 33750350446 scopus 로고    scopus 로고
    • Cauchy problem for the Vlasov-Poisson-Boltzmann system
    • Yang T., Yu H. J., Zhao H. J.: Cauchy problem for the Vlasov-Poisson-Boltzmann system. Arch. Ration. Mech. Anal. 182, 415-470 (2006).
    • (2006) Arch. Ration. Mech. Anal. , vol.182 , pp. 415-470
    • Yang, T.1    Yu, H.J.2    Zhao, H.J.3
  • 33
    • 33750343166 scopus 로고    scopus 로고
    • Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system
    • Yang T., Zhao H.-J.: Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system. Commun. Math. Phys. 268, 569-605 (2006).
    • (2006) Commun. Math. Phys. , vol.268 , pp. 569-605
    • Yang, T.1    Zhao, H.-J.2


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